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But how do clutch plates grip if they're oil soaked? Not intuitive.
Short answer:
The friction material is rough and porous so spring pressure pushes the oil out of the way through the gaps and channels - allowing the “teeth” of the friction material to grip.


long answer:
Interesting question. It is to do with asperity and the different forms of lubrication (boundary, mixed and hydrodynamic)
Sliding surface grip depends on asperity, the tiny peaks on a “smooth” surface.
On a steel bearing surface, asperities are very small; enough to hang on to oil molecules but small enough for oil molecules to flood them eliminating the hills and valleys producing a nice smooth film to ride on (tribological film).

Friction material has large asperities, too big for oil molecules to fill/bridge during low speed contact.

Speed is important - what’s called the Stribeck curve.
So on initial contact the surfaces are travelling at high speed relative to each other and this maintains a film. Not much torque is transmitted as it’s just oil film on oil film (hydrodynamic).
With more pressure oil gets displaced through the hills and valleys and asperities begin to contact, but there are reservoirs of oil molecules in the valleys to re-coat them - this is the “mixed“ regime.

The two surfaces start to become matched in speed and some torque is transferred. As relative speed reduces and/or pressure increases the oil has an easy way out on a rough clutch that it doesn’t have with smooth bearings - so the clutch asperities clear and break through the film far earlier and you get direct dry contact on interlocking hills and valleys of the plates.

You still get reduced wear and debris cleaning, the other functions of lubrication.
 
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